The quantitative study of how fluids (gases and liquids) move.

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27 views

The free surface of the wave is a material surface

If we define the free surface by: $F(x,y,t)=y-h(x,t)=0$ Then for this to be a material surface $\frac{DF}{Dt}=0$ on $y=h(x,t)$ However on $y=h(x,t)$, $F=0$, so doesn't this just imply ...
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0answers
427 views

Static pressure in relation to CFM

I’ve scoured the internet in search of an answer to no avail, so it’s time to ask the experts! My background is more Chemistry and Biology, not Physics, or specifically fluid dynamics, so bear with ...
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2answers
62 views

Eulerian mass conservation on a stream line to Lagrangian mass conservation

if the density of a fluid particle is conserved on a streamline, $$\frac{d\rho}{dt}=0.$$ Why does this mean $$\frac{\partial \rho}{\partial t}+(\mathbf{v}\cdot\nabla)\rho=0$$ is true everywhere? Why ...
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2answers
339 views

Given airplane mass, velocity of air under wing, and a wing area, find velocity of air over wing

I attempted to solve this problem as a tutor for a student and struggled, but want to be convince the professor didn't provide enough information. The problem is essentially: We wish to maintain a ...
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1answer
172 views

Metric inside a sphere of uniform density?

Is an exact solution to Einstein's Field Equations known for the interior of a sphere of uniform density (to approximate a star or planet, for example?)
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8answers
1k views

Why does an ice cube not twirl along when twirling a drink glass?

When you have a drink with an ice cube and twirl the glass, the liquid itself seems to twirl but the ice cube stays roughly in the same place. Why is this?
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2answers
386 views

Backwards airflow in a Venturi tube

When air is flowing through a Venturi tube, it's speed increases at the narrow section. If the airflow is arranged by moving the Venturi tube through calm air, this means air will momentarily flow ...
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1answer
3k views

Fluid in a rotating cylinder

I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically?
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30 views

How can a rotating cylinder produce lift? [duplicate]

In the air, the velocity and angular momentum that causes a force against gravity is lift. How can a rotating cylinder make lift with angular momentum?
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1answer
55 views

Can the fluid volume in a control volume change over time?

For a control volume, am I right in thinking it's just the boundary of the volume that is fixed? The volume of fluid inside the control volume can change, over time?
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34 views

The velocity of air on an airfoil

They say that velocity of the top layer on an airfoil is higher than the lower layer. But, according to the continuity principle of fluid, the velocity of air is inversely proportional to the surface ...
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1answer
67 views

Does air speed vary in a jet engine axial flow compressor?

Does it get slower and slower after each stage because of the pressure increase? Or does the shrinking of the space after each stage compensate for this and the air speed at the last stage of the ...
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6answers
99k views

Relation between pressure, velocity and area

In a nozzle, the exit velocity increases as per continuity equation $Av=const$ as given by Bernoulli equation (incompressible fluid). Pressure is inversely proportional to velocity, so we have lower ...
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1answer
31 views

How do we force a turbulent fluid to keep the input energy rate equal to energy dissipation rate?

If I want to do a DNS (direct numerical simulation) for turbulent fluid, and I know $\nu$, how can I add an external force so that the input energy rate is equal to the energy dissipation rate? If ...
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3answers
184 views

Why do nuclear weapons create a blast wave?

As far as I know, in a nuclear explosion the energy is released in the form of radiation (neutrons, gamma rays, alpha particles and electrons), light and heat. There isn't a chemical reaction that ...
3
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1answer
525 views

What is the return probability for Brownian motion in three dimensions?

I would like to know the probability of return to the initial point in three dimensional Brownian motion. Does someone know an expression for the diffusion constant? (Suggestions of books on this ...
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1answer
140 views

Using the continuity equation against gravity

Studying Fluid Mechanics right now and in my textbook there is an example of getting water up to a bathroom in a house. We're given the diameter of the inlet pipe and bathroom pipe, but only the ...
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63 views

Expected value, Fluid Mechanics and Momentum balance

I've been doing some problems on Fluid Mechanics involving the balance of Matter and Momentum and I have a question I've been wondering about. Suppose the following: We have a (viscous and ...
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1answer
107 views

How to find the force due to fluid pressure over a surface?

The question is about sphere like surfaces, like the hemispherical base of a cylinder as shown. The cylinder is filled with fluid till the given height $h$, and the density of the fluid is $\rho$ ...
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1answer
591 views

Why viscosity is diffusive?

I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion ...
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2answers
529 views

Capillary action and its limitations

From Wikipedia Capillary Action Thus for a 4 m diameter glass tube in lab conditions given above (radius 2 m), the water would rise an unnoticeable 0.007 mm. However, for a 4 cm diameter tube (radius ...
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0answers
43 views

How big is the power loss of a downwind wind turbine due to turbulence created by an upwind turbine?

When a horizontal axis wind turbine is placed downwind of another horizontal axis wind turbine (distance between the two is minimal), then the downwind wind turbine has a lower power output because of ...
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1answer
936 views

Derivation of Archimedes' principle

It is my understanding that upthrust from a liquid on a body is due to pressure difference on the top of the body and the bottom of the body. How, then, is this fact used in order to derive/work out ...
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1answer
78 views

How can I carry out this force summation? Control volume involved

I have a stationary jet engine on a test stand, like shown in the next figure: The control volume is indicated in the figure as a dashed rectangle, that has its left side far upstream of the ...
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1answer
44 views

ϕ-component of equation of moition: proving a relationship [closed]

I have the following velocity vector (in spherical polars): \begin{equation} \textbf{v} = u \hat{\textbf{r}} + v_{\phi}\hat{\boldsymbol\phi} \end{equation} Where $u(r) = u$ and $v_{\phi} (r) = ...
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1answer
410 views

Difference between a “source dipole” and a “force dipole”

I know quite well what a dipole is and in general what multipole moments are (in the context of, for instance, electrodynamics). What I find myself confused by is something called a "force dipole" in ...
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175 views

Self-made air pump - What does it take to pump up a balloon?

We are building a simple altitude-controlled balloon (idea borrowed from Google Loons). As part of that, we need an air pump to inflate a balloon acting as ballast (which is called a Ballonet in ...
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0answers
37 views

Calculating power in fluid systems with $pQ.$

I was wondering: say we have a fan which is being used to provide lift to some mass, like in a simple air cushion device, where the air has to flow through a chamber beneath the fan. Let's say that ...
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1answer
92 views

How are shock waves related to sound, and are there equations describing its density, size, and pressure?

How exactly does one model a shock wave? I've done a lot of searching and have failed to find any equations where we're able to relate things such as its pressure, density, temperature etc. I've ...
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1answer
127 views

Water clock in ancient time [closed]

A Water clock used in ancient Greek is designed as a closed vessel with a small orifice O.The time is determined according to the level of the water in the vessel. What should the shape of the vessel ...
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0answers
23 views

Roughness of the Surface and the time that a toy hovercraft hovers?

My question is about a toy CD hovercraft. I want to know that how does the time that the hovercraft hovers scale with roughness of the surface? Thanks in advance
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1answer
131 views

What's up with my whipped cream? [closed]

I got a latte with whipped cream this morning, and towards the end of the drink I noticed a peculiar effect. Regardless of how I turned the cup and thereby the coffee, the whipped cream pieces ...
2
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1answer
248 views

The demise of the Tacoma Narrows bridge was casused by aeroelastic flutter. But isn't that just a special case of resonance?

Much of the research I've done on the Tacoma Narrows bridge disaster of 1940 attribute the collapse of the bridge due to aeroelastic flutter - not strucural resonance. But isn't aeroelastic flutter ...
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3answers
2k views

How to relate speed of sound with relative humidity?

I am exploring the idea of measuring the humidity of a space using sound waves, however I am having trouble finding a mathematical relationship between the speed of sound and the humidity level. ...
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2answers
787 views

Considerations and questions for a DIY heat pipe; how to choose a working fluid? [closed]

I plan to build a DIY heat pipe! For more info on what a heat pipe is, see Wikipedia. I would like to use it to cool a desktop graphics card I have. I am having trouble deciding how to choose the ...
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1answer
33 views

Conceptualising the switch from discrete molecules to the continuum (fluid dynamics)

I understand that $\rho(x,t)$ represents the density of the small volume surrounding the point $x$. However what have I done with the discrete molecules in the process of averaging?
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2answers
150 views

Mass flux across a volume

Here mass flux means the mass flow rate, units: kilograms/second This is for a one-dimensional flow Firstly is the reason why the mass flux/ mass flow rate $=$ $\rho(x_1,t)A(x_1,t)u(x_1,t)$ ...
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2answers
89 views

Deriving an Euler Equation

In this derivation is it necessary to write the triple integral, as I thought that if we are dealing with one fluid particle it only contains one "point" and hence we do not have to take a sum?
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1answer
433 views

How does the divergence theorem justify the integral form of the continuity equation?

I vaguely understand the continuity equation (at least its integral form), but I don't really understand the differential form of the continuity equation. I'm having trouble understanding how to ...
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1answer
1k views

What does the continuum hypothesis of fluid mechanics mean?

I'm a bit confused by the continuum hypothesis stating that fluid are continuous objects rather than made out of discrete objects. Say for $\rho (x,t)$ (density) is there more than one fluid ...
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1answer
37 views

Pressure as the magnitude of the reaction force

Here $\vec{F}$ is the reaction force caused by the interaction of the fluid particle on the surface and another. I don't think the two parts I have highlighted in green tally with one another. If ...
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1answer
499 views

Continuity equation in fluid mechanics

The continuity equation in fluid mechanics states that $$ \frac{\partial\rho}{\partial t} + \nabla\cdot(ρ\mathbf u)=0 $$ Can you explain to me what is the physical meaning of each term of the ...
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1answer
193 views

Is the Mass flow rate (Mass flux) a scalar quantity?

Wikipedia states that mass flow rate is a scalar quantity, however Mass Flow Rate= Density x Cross Sectional Area x Velocity and velocity is a vector quantity, so this would imply Mass Flow Rate is ...
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1answer
166 views

Rate of Dripping of tube

My original problem was to discover the rate at which leaking taps dripped, and its relation with the tap's size, radius, etc. However, I have no clue how taps work, so I simplified the problem. ...
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1answer
462 views

Dependence of streamlined flow on viscosity

My teacher told true class the following statement:- Streamlined flow is more likely for liquid with more viscosity as sturdy flow can only be achieved with slow speed. It's true that viscosity ...
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1answer
32 views

What to measure for cylinder stiffness/compressibility?

I have 2 cylinders made from different polymers. Both cylinders are made to 'accept' the same volume of water. When I fill cylinder 1 it is subjectively stiff while cylinder 2 is subjectively floppy. ...
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0answers
148 views

Where can I find a table for NIST standards on temperature and pressure?

The Wikipedia article Standard conditions for temperature and pressure notes that IUPAC and NIST are two of the most common standards for temperature and pressure in use. Even if I could have gotten ...
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3answers
114 views

Walking on water

I was wondering about walking on water. I wonder if we can use surface tension to do this. Lets say I make a pair of shoes in shape which has infinite perimeter (e.g a koch snowflake) with glass. Now ...
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48 views

What will happen to this fan in this situation?

Lets say I have a pipe with a fan at the end of it and it is drawing ambient air from the other end of the pipe. Once I account for some blockages and looking at the fan curve, it was found the ...
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1answer
78 views

Boundary Layer in aerofoil

I want to know how the top and bottom boundary layer interact at the trailing edge of an aerofoil (zero angle of attack) and what happens to the boundary layer after a small distance from the trailing ...